Differentiation of SRB states for hyperbolic flows
By David Ruelle. Ergodic Theory and Dynamical Systems, 2004
50 citations recorded by the source corpus.
Abstract Let the ${\cal C}^3$ vector field ${\cal X}+aX$ on M define a flow (fat) with an Axiom A attractor Λa depending continuously on a∈(−ϵ,ϵ). Let ρa be the SRB measure on Λa for (fat). If $A\in {\cal C}^2(M)$, then $a\mapsto \rho _a(A)$ is ${\cal C}^1$ on (−ϵ,ϵ) and dρa(A)/da is the limit when ω→0 with Im ω>0 of \[ \int _0^\infty e^{i\omega t}\,dt \int \rho _a (d x)\,X(x)\cdot \nabla _x(A\circ f_a^t). \]
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/b37b4cd0754ba5d6eddd108e4e3b3cd748354f61
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
- David Ruelle
- Viviane Baladi
- Michael Ghil
- Mickaël D. Chekroun
- Eric Simonnet
- B. Saussol
- C. Liverani
- Gary Froyland
In Statistical and Nonlinear Physics
- David Ruelle
- Michael Ghil
- Viviane Baladi
- Mickaël D. Chekroun
- Eric Simonnet
- B. Saussol
- C. Liverani
- Valerio Lucarini
Citations in the corpus
- A review of linear response theory for general differentiable dynamical systems (2009, methodology): “This is proved in [ 42 ], using the machinery of Markov partitions.”
- Linear response, or else (2014, background): “In the present note, we do not discuss linear response for continuous time dynamics [50, 17], or for dynamical systems in infinite dimensions (such as coupled map lattices [27, 28]).”
- Stochastic climate dynamics: Random attractors and time-dependent invariant measures (2011, background): “For hyperbolic deterministic systems, precise estimates exist for the response of their SRB measures to perturbations [53, 54].”